Recent hyperspectral applications demand for higher accuracy and speed. This thesis develops a hyperspectral application analysis solution to address challenges in the different steps of denoising, order selection and unmixing of hyperspectral application data. Currently, all these steps process the data in cascade to achieve the optimum results. While in existing approaches the desired criterion is different in these steps, the proposed simultaneous Denoising and Intrinsic Order Selection (DIOS) method unifies these criteria. This property not only makes more sense for the desired optimization problem, but also leads to a faster processing algorithm. Consequently, DIOS avoids possible error propagation from the denoising stage to the dimension estimation stage, leading to more accurate results. The proposed method is based on minimizing the estimated Mean Square Error (MSE). The success rate of existing dimension estimation methods declines with the increase of image dimension and the decrease of Signal-to-Noise Ratio (SNR). The most competitive method fails to detect the correct dimension in 30% of cases around 2dB. However, in simulation results DIOS is shown to be successful with a failure rate of about 5%. The proposed unmixing method, based on a simple least square estimation, improves the speed performance least 10 times for an average-sized data cube of 2MB. Compared to some well known existing approaches, the unmixing method improves the estimated MSE up to 60% for SNR<10dB. A new whitening process for hyperspectral applications with coloured noise is also proposed. Since the proposed method avoids the inversion of large matrices, computational complexity is substantially decreased. In the presence of coloured noise, simulation results show that the proposed whitening method lowers the MSE of unmixing and outperforms the existing whitening methods particularly when the noise correction factors increase.